Conformational properties of α- and β-azabicyclane opiates. The effect of conformation on pharmacological activity

Conformational energy calculations using the MM 2 (molecular mechanics II) program are reported for diastereoisomeric α- and β-azabicyclanes (3-methyl-9-methoxy-9-phenyl-3-azabicyclo [3.3.1] nonanes) which are prototypical phenyl-axial and phenyl-equatorial opiates. After energy minimization, both compounds are found to prefer a chair–chair conformation of the piperidine and cyclohexane rings with two mirror image orientations of the phenyl and methoxyl groups. The calculations also indicate that the equilibrium conformations of the phenyl and methoxyl groups are very similar in the two diastereoisomers. A morphine-like conformation of the phenyl group was found to be very unfavorable because of a high barrier to rotation of the phenyl group. This does not have an apparent effect on opiate agonist properties, but does result in a significant weakening of the antagonist activity of the N-allyl derivative of α-azabicyclane. This is discussed in terms of a model for phenyl-axial and phenyl-equatorial opiate substrates which accounts for both similarities and differences in their structure–activity relationships. A detailed comparison is also made between the computed structures and those observed by x-ray crystallography with excellent agreement between the two.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

A CW ultrasonic bolt-strain monitor

There exists a need for a relatively inexpensive system for measuring strain in bolts. The torque wrench is one technique for straining bolts which has been widely applied. Unfortunately, friction in the bolt threads and between the nut and the work tend to make such a simple system inaccurate. In practice, a torque wrench is unacceptable for many situations where strain is critical. In this article, an ultrasonic technique is described which can indicate changes in bolt strain to better than one part in 10⁴. The technique is based on the one-dimensional propagating-ultrasonic-wave model and uses a new ultrasonic instrument called a Reflection Oscillator Ultrasonic Spectrometer which is a closed-loop feedback marginal-oscillator system that frequency locks the device to the peak of a mechanical resonance in the bolt. The instrument indicates a shift in the bolt resonance frequency due to elongation and changes in velocity of sound due to strain. Data are presented comparing a standard torque wrench to the ultrasonic monitor for different measured stresses on the bolt as well as for different bolt conditions. The strain instrument can be used to monitor changing stresses, to measure material properties and may be applied as a strain gage or load cell.     

On shifted Eisenstein polynomials

We study polynomials with integer coefficients which become Eisenstein polynomials after the additive shift of a variable. We call such polynomials shifted Eisenstein polynomials. We determine an upper bound on the maximum shift that is needed given a shifted Eisenstein polynomial and also provide a lower bound on the density of shifted Eisenstein polynomials, which is strictly greater than the density of classical Eisenstein polynomials. We also show that the number of irreducible degree \(n\) polynomials that are not shifted Eisenstein polynomials is infinite. We conclude with some numerical results on the densities of shifted Eisenstein polynomials.     

Wiring of redox enzymes on three dimensional self-assembled molecular scaffold

The integration of biological molecules and nanoscale components provides a fertile basis for the construction of hybrid materials of synergic properties and functions. Stable protein 1 (SP1), a highly stable ring shaped protein, was recently used to display different functional domains, to bind nanoparticles (NPs), and to spontaneously form two and three-dimensional structures. Here we show an approach to wire redox enzymes on this self-assembled protein-nanoparticle hybrid. Those hybrids are genetically engineered SP1s, displaying glucose oxidase (GOx) enzymes tethered to the protein inner pore. Moreover, the Au-NP-protein hybrids self-assembled to multiple enzymatic layers on the surface. By wiring the redox enzymes to the electrode, we present an active structure for the bioelectrocatalytic oxidation of glucose. This system demonstrates for the first time a three-dimensional assembly of multiple catalytic modules on a protein scaffold with an efficient electrical wiring of the enzyme units on an electrode surface, thus implementing a hybrid electrically active unit for nanobioelectronic applications.     

A radical determined by a class of almost nilpotent rings

Acta Mathematica Hungarica -